100 should be the correct answer.
We have 125 Cricket Players, 130 Hockey Players & 135 Basketball Players.
Thus we have total (125 + 130 + 135) = 390 game players.
In the class we have 145 Player students & 5 non player students.
Each of these 145 Player students plays at least one of these 3 games( otherwise he/she would come in non player's category),
Now out of these 145 Players students we will have some 1 game players, some 2 game players and some 3 game players.
That is each of the player student can be either a 1 game players, or a 2 game player or a 3 game player.
Also all of these 145 players students will make up 390 game players.
Now suppose if all 145 students are 1 game players, then we will have 145 x 1 = 145 game players.
suppose if all 145 students are 2 game players, then we will have 145 x 2 = 290 game players,
suppose if all 145 students are 3 game players, then we will have 145 x 3 = 435 game players.
It is clear that to make 390 game players out of 145 player students, we need some 3 game player students also, because even if all of 145 students were 2 game players then also we can have only 145 x 2 = 290 players at most, and we are still 100 game players away from given 390 players hence we need at least (390 - 290) = 100, 3 game player students out of 145 player students using pigeon - hole principle.
(125 + 130 + 135) % 145 = 100